LETTER FROM THE EDITOR-IN-CHIEF
University of Oxford
I hope you had an enjoyable summer and that you managed to make the most of any respite.
The theme of the ﬁrst three papers in this issue of The Journal of Computational Finance is expansions and semi-analytical approximations. In particular, these papers show how certain state-of-the art methods for standard derivatives can be extended to more complex models or contracts, including barrier features and path dependency.
In our ﬁrst paper, “Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach”, Jerome Lelong presents a new version of the Longstaff–Schwartz algorithm in which the conditional expectations are computed using Wiener chaos expansion. This approach allows the pricing of path-dependent Bermudan options and can be parallelized efﬁciently.
Following this, we have “On extensions of the Barone-Adesi and Whaley method to price American-type options”. Here, Ludovic Mathys provides two extensions of the quadratic approximation scheme of Barone-Adesi and Whaley to approximate the price of American-type options: namely, under jump diffusion or with barrier features. The author derives a perturbation method to approximate solutions of a free boundary problem satisﬁed by the early exercise premium, and he demonstrates the accuracy and efﬁciency of the method through numerical tests.
In the issue’s third paper, “Pricing multiple barrier derivatives under stochastic volatility”, Marcos Escobar, Sven Panz and Rudi Zagst derive pricing formulas for options on multiple underlying assets with multiple barriers and including a speciﬁc common stochastic volatility process. The authors use numerical tests to compare semi-analytical formulas against Monte Carlo results.
Finally, Aleksey Minabutdinov, Ilya Manaev and Maxim Bouev present an efﬁcient approach to the problem of ﬁnding the best approximation to a foreign exchange market covariance matrix in “Finding the nearest covariance matrix: the foreign exchange market case”. Here, the authors address the necessary degeneracy resulting from no-arbitrage conditions by a dimension reduction and demonstrate the advantages of this approach in numerical tests.
I wish you an interesting read.
The authors consider the problem of finding a valid covariance matrix in the foreign exchange market given an initial nonpositively semidefinite (non-PSD) estimate of such a matrix.
This work generalizes existing one- and two-dimensional pricing formulas with an equal number of barriers to a setting of n dimensions and up to two barriers in the presence of stochastic volatility.
Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach
In this work, the authors propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process.
This paper provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models and American barrier-type options under the Black–Scholes framework.